Office:
Office hours for the Spring 2015 semester:
Wednesday: noon to 3:00 PM and by appointment.
Room 319 of the Farris Engineering Center (FEC).
Located near the northeast corner of
Central Avenue and University Boulevard.
This is building #119 in section J-17 of the
central campus map.

NonEuclid: by Joel Castellanos, Joe Austin, Ervan Darnell, and Maria Estrada
Interactive Java software for creating
ruler and compass
constructions in both the Poincaré Disk and the Upper Half-Plane Models
of Hyperbolic Geometry. The software allows students to gain experience in Hyperbolic Geometry and
to empirically investigate questions such as: "In Hyperbolic Geometry, are the base angles of an
isosceles triangle congruent?" The software and documentation are accessible to anyone with high
school level geometry.

Fractal Grower: by Joel Castellanos
Fractal Grower is Java software for growing Lindenmayer substitution (L-systems) fractals.
In its default mode, the software displays an
interface for simple L-Systems which can be modeled by paper folding. This interface is
appropriate for teaching fractals to elementary and middle school students.

The full L-System interface (selectable by menu) is more appropriate for high school
and university students.
An L-system is a formal grammar (a set of rules and symbols) most famously used to model
the growth processes of plants. Changes to the library of preset parameters
will quickly yield beautiful fractal images of such variety that it is unlikely that
what you create has ever been seen before.

For grade school students, it is a fun way to practice prime factorization of
composite numbers.

For beginning programming students, it is chance to develop software with an
actual, living, generally friendly, user base. It is a change to contribute
to an on-going, open-source programming project. It is a chance to do homework that,
asside from helping you learn,
has an additional, small positive influence in the world.

For teachers, it is a prototype, designed for college freshman, of what might be a
new trend in education: Methods that enhance the learning experience by being at once
well constructed programming exercises and productive of real-world value.

DFIELD & PPLANE: by John C. Polking, David Arnold and Joel Castellanos
This software is designed as a companion for 'Ordinary Differential Equations
using MatLab' by David Arnold & John C. Polking. DFIELD graphs the direction field of single,
first order differential equations. PPLANE graphs the direction field in the phase plane of
autonomous systems. PPLANE also graphs linearizations about equilibrium points, stable and unstable
orbits, nullclines, and allows the user to view solutions in three dimensions. Both DFIELD and
PPLANE solve differential equations with a selection of numerical solvers, and allow the user to
choose parameters of those solvers.

My role in this project consisted of integrating student feedback into the early MatLab
version while teaching the laboratory section of the first class in which the software was used.
I then ported the MabLab version to Java.

Games:

Polyomino: http://polyomin.org/ by Luke Balaoro, Joel Castellanos and Ezra Stallings
Poyomino is a simple, web-based puzzle game that plays with building higher order polyominos from lower order
monominos, dominos, trominos, tetrominos (the 5 Tetris blocks), pentominos, hexominos, heptominos, and up through octominos.

Abstract: The U.S. Air Force Space and Missile Systems Center (SMC) at the ground systems Research,
Development, Test, and Evaluation (RDT&E) Support Complex (RSC) located at Kirtland AFB,
has developed an in-house Trending Tool system. The system is used for archiving, graphing,
and statistical analysis of State of Health (SOH) telemetry to support anomaly resolution and
long-term trend analysis. This presentation examines strategies for user navigation
through the very large data space, and a general case for small group development of
in-house software rather than using Commercial Off-the-Shelf (COTS) software. In particular,
the SOH telemetry, as opposed to general data, exhibits distribution qualities that allow for
specialized data management. Furthermore, user access patterns have been identified across
multiple satellite missions that can be leveraged to significant advantage.

Abstract: A fully automatic method of synthesizing isotropic textures on subdivision
surfaces from sample images is presented. Both Gaussian and Laplacian pyramid representations
of the sample texture are constructed. Texture synthesis proceeds coarse-to-fine, by incrementally
inverting the Laplacian pyramid to produce an initial guess and refining this guess using
non-parametric sampling. The sampling procedure uses a nearest neighbor search while preserving
first-order statistics. The resulting texture is generated directly on the subdivision surface.
Within the domain of isotropic textures, the proposed method offers improvements in faithful
reproduction of a sample's appearance over a wide range of scales. The method can also be
used to produce isotropic variants of anisotropic textures. Finally, while the sampling
procedure we describe is not amenable to standard methods for nearest neighbor search
in high dimensional spaces, an acceleration method is proposed that uses an
eigenvector transform and a set of dynamic Kd-trees.

Abstract: This article represents an example of how computer software can be used to facilitate collaborative learning and the integration of mathematics and science. "Snap shots" from a pilot project, with thirty high school juniors who were involved in a university summer program, reveal how student-centered learning is facilitated by technology. This exploratory trial provides a glimpse of what the "classroom after next" might look like utilizing groupware in instructional settings.

Abstract: This paper introduces a new software tool, NonEuclid, which enables the user to easily perform ruler and compass constructions and measurements in Hyperbolic Geometry. The paper demonstrates how the software can be used to explore geometric patterns and theorems in Hyperbolic Geometry, as well as help to teach an axiomatic approach to geometry in general. A study of Hyperbolic Geometry can help students break away from long held pictorial definitions of geometric objects by offering a world in which the pictures are all changed; thereby helping students focus on the exact words in formal definitions of familiar objects such as squares, isosceles triangles, rhombuses.

Abstract: The paper presents an out-of-class writing method for helping students understand and internalize scientific concepts and theories. The proposed method breaks sharply form the typical writing assignments of summery reports and research papers. In particular, it focuses on careful student critiques of small segments of the given textbook, question articulation, development interconnections between class topics and concepts from other classes or life experience, student generated thought experiments, and imagination. The paper includes instructor guidelines and student hand-outs.